mat: added a few godoc examples for Dense methods (#263)

* added a few godoc examples for Dense methods

mat/dense_example_test.go

@@ -0,0 +1,130 @@
+// Copyright ©2017 The gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package mat_test
+
+import (
+	"fmt"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleDense_Add() {
+	// Initialize two matrices, a and b.
+	a := mat.NewDense(2, 2, []float64{1, 0, 1, 0})
+	b := mat.NewDense(2, 2, []float64{0, 1, 0, 1})
+
+	// Add a and b, placing the result into c.
+	// ...Notice that the size is automatically adjusted when the receiver has zero size.
+	var c mat.Dense
+	c.Add(a, b)
+
+	// Print the result using the formatter.
+	fc := mat.Formatted(&c, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\nc = %v\n\n", fc)
+	// Output:
+	// Result:
+	// c = ⎡1  1⎤
+	//     ⎣1  1⎦
+	//
+}
+
+func ExampleDense_Sub() {
+	// Initialize two matrices, a and b.
+	a := mat.NewDense(2, 2, []float64{1, 1, 1, 1})
+	b := mat.NewDense(2, 2, []float64{1, 0, 0, 1})
+
+	// Subtract b from a, placing the result into a.
+	a.Sub(a, b)
+
+	// Print the result using the formatter.
+	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\na = %v\n\n", fa)
+	// Output:
+	// Result:
+	// a = ⎡0  1⎤
+	//     ⎣1  0⎦
+	//
+}
+
+func ExampleDense_MulElem() {
+	// Initialize two matrices, a and b.
+	a := mat.NewDense(2, 2, []float64{1, 2, 3, 4})
+	b := mat.NewDense(2, 2, []float64{1, 2, 3, 4})
+
+	// Multiply the elements of a and b, placing the result into a.
+	a.MulElem(a, b)
+
+	// Print the result using the formatter.
+	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\na = %v\n\n", fa)
+	// Output:
+	// Result:
+	// a = ⎡1   4⎤
+	//     ⎣9  16⎦
+	//
+}
+
+func ExampleDense_DivElem() {
+	// Initialize two matrices, a and b.
+	a := mat.NewDense(2, 2, []float64{5, 10, 15, 20})
+	b := mat.NewDense(2, 2, []float64{5, 5, 5, 5})
+
+	// Divide the elements of a by b, placing the result into a.
+	a.DivElem(a, b)
+
+	// Print the result using the formatter.
+	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\na = %v\n\n", fa)
+	// Output:
+	// Result:
+	// a = ⎡1  2⎤
+	//     ⎣3  4⎦
+	//
+}
+
+func ExampleDense_Inverse() {
+	// Initialize two matrices, a and ia.
+	a := mat.NewDense(2, 2, []float64{4, 0, 0, 4})
+	var ia mat.Dense
+
+	// Take the inverse of a and place the result in ia.
+	ia.Inverse(a)
+
+	// Print the result using the formatter.
+	fa := mat.Formatted(&ia, mat.Prefix("     "), mat.Squeeze())
+	fmt.Printf("Result:\nia = %.2g\n\n", fa)
+
+	// Confirm that A * A^-1 = I
+	var r mat.Dense
+	r.Mul(a, &ia)
+	fr := mat.Formatted(&r, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\nr = %v\n\n", fr)
+
+	// The Inverse operation, however, is numerically unstable, and should typically be avoided.
+	// For example, a common need is to find x = A^-1 * b. In this case, the SolveVec method of VecDense
+	// (if b is a Vector) or Solve method of Dense (if b is a matrix) should used instead of computing
+	// the Inverse of A.
+	b := mat.NewDense(2, 2, []float64{2, 0, 0, 2})
+	var x mat.Dense
+	x.Solve(a, b)
+
+	// Print the result using the formatter.
+	fx := mat.Formatted(&x, mat.Prefix("    "), mat.Squeeze())
+	fmt.Printf("Result:\nx = %v\n\n", fx)
+
+	// Output:
+	// Result:
+	// ia = ⎡0.25    -0⎤
+	//      ⎣   0  0.25⎦
+	//
+	// Result:
+	// r = ⎡1  0⎤
+	//     ⎣0  1⎦
+	//
+	// Result:
+	// x = ⎡0.5    0⎤
+	//     ⎣  0  0.5⎦
+	//
+}